Question:medium
If \( a, b, c \) are in A.P. and if the equations \( (b - c)x^2 + (c - a)x + (a - b) = 0 \) and \( 2(c + a)x^2 + (b + c)x = 0 \) have a common root, then
If \( a, b, c \) are in A.P. and if the equations \( (b - c)x^2 + (c - a)x + (a - b) = 0 \) and \( 2(c + a)x^2 + (b + c)x = 0 \) have a common root, then
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When equations share a common root, substitute the root and use the A.P. condition to simplify. Check the resulting sequence for A.P. or G.P.
Updated On: Nov 28, 2025
- \( a^2, b^2, c^2 \) are in A.P.
- \( a^2, c^2, b^2 \) are in A.P.
- \( c^2, a^2, b^2 \) are in A.P.
- \( a^2, b^2, c^2 \) are in G.P.
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